The pre-match gesture in support of the Black Lives Matter movement has been a part of the Premier League and English Football League games since football resumed after the coronavirus shutdown in June.
Racist abuse of footballers on social media has been widespread in recent weeks, but many voices in the game believe the gesture is no longer having the effect that it originally did.
“Fighting all forms of discrimination and creating an equal, inclusive society is something that we feel very passionately about,” Cook said in a club statement ahead of Saturday’s Championship match against Queens Park Rangers.
“But that is defined by much more than a gesture, which we feel has run its course and is no longer having the effect it first did eight months ago.
“As footballers and role models we want to continue affecting change in a positive way but we also need support - from governing bodies and social media platforms, in particular - and want to see action rather than words or gestures.”
Crystal Palace forward Wilfried Zaha recently said that taking a knee before matches is “degrading”, while Championship side Brentford decided last week they would stop making the gesture and look for new ways to support racial equality.
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